Control Valves · Flow Coefficient · Valve Sizing
Control Valve Flow Coefficient (Cv and Kv): What It Is, How It Works and How to Calculate It
A complete practical guide to the control valve flow coefficient: what Cv and Kv mean, how they are defined and measured, the sizing formulas for liquids and gases, worked calculation examples, an interactive calculator, cavitation and choked flow explained, and why Cv is the most important number in valve selection.
Control Valve Flow Coefficient (Cv)?
Every control valve in a process plant has one number that defines its fundamental hydraulic capability: the flow coefficient, expressed as Cv in the American (imperial) system and Kv in the international (metric) system. This single number tells you exactly how much flow the valve can pass at a given pressure drop, in a standardised and comparable way that works across every manufacturer and every valve type.
Without understanding Cv, you cannot correctly size a control valve, interpret a valve datasheet, understand why a valve is hunting at low openings, or explain why a system is not delivering the required flow. It is the most important single parameter in control valve engineering, yet it is surprisingly poorly explained in most introductory resources.
This guide explains Cv and Kv completely: what they mean physically, how they are derived, the sizing formulas for both liquid and gas service, worked calculation examples with real numbers, and the critical phenomena of cavitation and choked flow that occur when a valve is pushed beyond its design limits. An interactive calculator is included so you can solve valve sizing problems instantly. For background on how control valves work mechanically, see our guide on what is a control valve and how it works.
What Is the Flow Coefficient (Cv)?
The flow coefficient Cv is defined as the volume flow rate of water (in US gallons per minute) that will pass through a valve with a pressure drop of exactly 1 psi across it, at a water temperature between 60°F and 80°F (15.5°C to 26.7°C).
In plain language: Cv is a measure of how much flow a valve lets through per unit of pressure drop. A valve with Cv = 10 passes 10 US gallons per minute of water for every 1 psi of pressure drop across it. A valve with Cv = 100 passes 10 times more flow for the same pressure drop. Higher Cv means a larger, more open or less restrictive valve.
Cv is not a fixed number for a given valve. It changes with valve opening position. A control valve at 100% open has its maximum Cv (called Cv max or Cv 100). At 50% opening it has a lower Cv. At 10% opening it has a much lower Cv. This relationship between opening position and Cv is called the valve characteristic and is one of the most important aspects of control valve selection. More on this below.
How Cv Is Measured: The Test Standard
The Cv value published on a valve datasheet is determined by physical testing according to a recognised standard. In North America and most international specifications, the governing standard is ANSI/ISA-75.02 (Control Valve Capacity Test Procedure). The equivalent international standard is IEC 60534-2-3.
The test procedure is straightforward:
- The valve is installed in a test rig with calibrated pressure taps upstream and downstream
- Water at 60°F (15.6°C) with a specific gravity of 1.0 is used as the test fluid
- The valve is set to a specific opening position (0%, 10%, 20% ... 100%)
- Flow and differential pressure are measured under steady-state conditions
- Cv is calculated from the measured flow and differential pressure using the liquid sizing formula
- This is repeated at each opening position to generate a complete Cv vs opening table
The Cv Liquid Sizing Formula: Derivation and Use
The fundamental Cv sizing formula for incompressible liquids (liquids and water-like fluids) comes directly from Bernoulli's equation and the continuity equation applied to the flow restriction inside the valve. The result is:
Where:
Q = Volumetric flow rate in US gallons per minute (GPM)
ΔP = Differential pressure across the valve in psi (P1 - P2)
SG = Specific gravity of the liquid relative to water at 60°F (water = 1.0) sqrt = square root
Rearranged to find flow rate given Cv:
Q = Cv × sqrt(ΔP / SG)
Rearranged to find required ΔP given Cv and Q:
ΔP = SG × (Q / Cv)²
Figure 1: The Cv formula relates the three measurable quantities at a valve: upstream pressure P1, downstream pressure P2 and volumetric flow rate Q. Given any two, you can find the third using Cv.
Why is there a square root?
The square root in the Cv formula comes from Bernoulli's equation. The kinetic energy of flow is proportional to the square of velocity (V²/2g). Flow through an orifice (which is what a partially open valve approximates) follows Torricelli's theorem: flow rate is proportional to the square root of the differential pressure. This means that to double the flow through a valve, you need to increase the differential pressure by a factor of four (2² = 4). Flow responds to the square root of the driving pressure, not linearly.
What Is Kv? The Metric Flow Coefficient
Kv is the metric equivalent of Cv. It is defined as the volume flow rate of water (in cubic metres per hour, m³/h) that passes through a valve with a pressure drop of exactly 1 bar across it, at a water temperature of 5°C to 40°C.
Where:
Q_m3h = Volumetric flow rate in cubic metres per hour (m³/h)
ΔP_bar = Differential pressure across the valve in bar
SG = Specific gravity of the liquid (water = 1.0)
Conversion between Cv and Kv:
Cv = 1.1560 × Kv (convert Kv to Cv)
Kv = 0.8646 × Cv (convert Cv to Kv)
| Parameter | Cv (American) | Kv (Metric / IEC) |
|---|---|---|
| Flow unit | US gallons per minute (GPM) | Cubic metres per hour (m³/h) |
| Pressure unit | psi (pounds per square inch) | bar |
| Test fluid | Water at 60°F (15.6°C) | Water at 5-40°C |
| Reference specific gravity | SG = 1.0 | SG = 1.0 |
| Governing standard | ANSI/ISA-75.01 | IEC 60534-2-1 |
| Typical use | North America, Middle East | Europe, Asia, International |
| Conversion | Cv = 1.156 × Kv | Kv = 0.8646 × Cv |
Cv and Kv Calculator: Interactive Tool
Use the calculator below to find the required Cv for your application, calculate the actual flow at a given Cv, or convert between Cv and Kv. Select the calculation mode using the tabs.
Worked Examples: Cv Calculations
Example 1: Find the required Cv for a water line
A 3-inch control valve must pass 80 GPM of water (SG = 1.0) with a maximum pressure drop of 15 psi. What Cv is required?
Example 2: Find the flow rate through a known valve at a given pressure drop
A control valve has Cv = 35 at its current 60% opening position. The differential pressure across it is 8 psi. The fluid is a light oil with SG = 0.85. What is the flow rate?
Example 3: Find the Cv/Kv for a metric application
A control valve must pass 12 m³/h of water (SG = 1.0) with a differential pressure of 0.5 bar. What Kv is required, and what is the equivalent Cv?
Oversized vs Undersized Control Valves: Why Cv Selection Matters
The Cv at the normal operating point determines whether the valve is operating at an appropriate percentage of its maximum travel. This is critically important for good process control.
| Condition | What it means | Consequence |
|---|---|---|
| Correctly sized | Normal flow passes at 40-70% valve opening. Maximum flow can be passed at around 80-85% opening. | Good controllability across the full operating range. The valve uses a healthy portion of its travel for normal control, leaving headroom for increased demand. |
| Oversized valve | Normal flow passes at very low opening (5-20%). A small stem movement produces a large flow change. | Very sensitive, difficult to control. The valve hunts (oscillates) because small valve movements cause large flow changes. The controller cannot maintain stable control. Common in plants where "safety margin" was added at every stage of valve selection. |
| Undersized valve | The required flow cannot be achieved even at 100% opening. The valve is the bottleneck in the system. | Process cannot reach target conditions. Valve is permanently at 100% open and provides no control. The only fix is replacement with a larger valve. |
Cavitation and Choked Flow: When Cv Calculations Break Down
The liquid sizing formula Cv = Q / sqrt(ΔP / SG) assumes single-phase, incompressible flow throughout the valve. In reality, two physical phenomena can make the actual flow deviate dramatically from what this formula predicts: cavitation and choked flow.
Figure 2: Pressure profile through a control valve. Pressure drops sharply at the restriction, reaching its minimum at the vena contracta (the narrowest point of the flow stream). Downstream of the vena contracta, pressure partially recovers to P2. If the minimum pressure at the vena contracta falls below the fluid vapour pressure, vapour bubbles form: this is the onset of cavitation.
What is cavitation?
As the fluid accelerates through the valve restriction, its pressure drops sharply to a minimum at the vena contracta (the narrowest point of the jet leaving the restriction). If this minimum pressure falls below the vapour pressure of the liquid at the flowing temperature, vapour bubbles (cavities) form in the liquid. As the fluid decelerates and the pressure recovers downstream, these bubbles collapse (implode) violently. Each implosion generates a micro-shockwave. Thousands of these implosions per second cause severe erosion of the valve trim (plug, seat and cage) in a very short time. The damage is visible as pitting, cratering and surface erosion on the metal surfaces.
Cavitation also causes noise (a crackling or gravel-like sound), vibration, and reduction in flow below what the Cv formula predicts. If you hear a crackling sound from a control valve handling liquids, cavitation is almost certainly occurring. See our related article on the control valve positioner for context on the complete valve assembly.
What is choked flow?
If the downstream pressure P2 is reduced far enough that the pressure at the vena contracta drops to and stays at the vapour pressure, the flow reaches a maximum that cannot be increased further by reducing P2. Even increasing the pressure drop to zero downstream. The vapour bubbles that form at the vena contracta occupy more volume (as gas) than the liquid they came from, effectively blocking the restriction and preventing further flow increase. This condition is called choked flow.
During choked flow, the actual flow is much lower than the Cv formula predicts because the formula assumes the full differential pressure P1 minus P2 is available to drive flow. Correct sizing for conditions approaching choked flow requires the use of the liquid pressure recovery factor (FL) in the sizing equations.
| Condition | Minimum pressure at vena contracta | Effect on flow | Valve damage? |
|---|---|---|---|
| Normal flow | Above vapour pressure Pv | Flow follows Cv formula accurately | No |
| Incipient cavitation | Reaches vapour pressure Pv | Flow begins to deviate from formula. Noise and vibration start. | Begins: slow erosion |
| Full cavitation | Below vapour pressure Pv, recovers above downstream | Flow significantly less than formula predicts. Severe noise. | Yes: rapid erosion of trim |
| Choked flow | Stays at or below vapour pressure throughout | Flow is independent of further ΔP increase. Maximum flow reached. | Yes: maximum erosion rate |
Valve Characteristics and How They Relate to Cv
A control valve's Cv does not change linearly with stem position. The relationship between valve opening (in %) and the ratio of actual Cv to maximum Cv is called the inherent characteristic of the valve. There are three standard characteristic types:
| Characteristic | Cv vs position relationship | Best for | Why chosen |
|---|---|---|---|
| Linear | Cv changes in direct proportion to stem position. At 50% open, Cv = 50% of Cv max. | Flow control with nearly constant pressure drop. Liquid level control. | Simple, predictable. The gain (change in Cv per % stem movement) is constant across the full range. |
| Equal Percentage | Each equal increment of stem position changes Cv by an equal percentage of its current value. Cv at 50% is typically 10-15% of Cv max. At 70% it is 25-30% of Cv max. | Most process control loops, especially where pressure drop varies with flow (pumped systems). | As flow increases and system pressure drop falls, the equal-percentage characteristic compensates, giving a more linear installed characteristic. The most widely used characteristic in process control. |
| Quick Opening | Large Cv change with small stem movement at low openings. Most of the flow range is covered in the first 30% of stem travel. | On/off service and pressure relief applications. Not for throttling or flow control. | Provides maximum flow quickly when the valve opens. The non-linear shape makes it unsuitable for modulating control but ideal for fast-acting on/off duty. |
Further Reading and External Resources
- Flowserve: Control Valve Handbook. The industry reference on control valve sizing, Cv calculation, cavitation, choked flow and valve characteristics. Available as a free PDF from one of the world's largest valve manufacturers.
- ISA-75.01.01: Control Valve Sizing Equations for Fluid Flow. The governing ISA/ANSI standard for liquid, gas and steam Cv sizing calculations including cavitation and choked flow correction factors.
- Emerson: Control Valve Sizing Tools and Resources. Free online Cv sizing tools and downloadable sizing software from Emerson, one of the leading global control valve suppliers.
- Inst Tools: Control Valve Design and Selection Factors. A useful companion overview of the broader control valve selection process including trim types, materials and body styles.
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What we learn today
- Cv is the flow coefficient that defines a control valve's flow capacity: the number of US GPM of water passing through the valve at 1 psi differential pressure. Kv is the metric equivalent (m³/h at 1 bar). The sizing formula is Cv = Q / sqrt(ΔP / SG). Both Cv and Kv change with valve opening position.
- A correctly sized valve operates at 40-70% opening under normal conditions. Oversized valves hunt and oscillate at low openings. Undersized valves cannot deliver the required flow even at 100% open. Add only a 30% safety margin to the calculated Cv when selecting a valve.
- Cavitation occurs when the pressure at the vena contracta inside the valve falls below the fluid vapour pressure. Vapour bubbles form and collapse violently, eroding the trim. Choked flow occurs when the pressure drop is so large that further reducing downstream pressure cannot increase flow further. Both conditions are identified by a crackling noise and flow below predicted values.
- Equal percentage is the most widely used valve characteristic in process control. Cv = 1.156 × Kv. Always confirm whether a supplier is quoting Cv or Kv before comparing valve sizes, as confusing the two results in a 15% error in flow capacity.